You don't specify if the "rumble" is related to engine RPM or vehicle speed.

If vehicle speed, you have wheel bearings (usually this shows up at higher speed), flex disk (again, this usually doesn't go away), suspension components, and differential.

If the engine RPM has anything to do with it, you could have exhaust system mounts, motor mounts, or even transmission mount, all of which can transmit noise to the chassis. If you have a hole forming in part of your exhaust, it would definitely sound like a "rumble", especially when you get on it from a stop since the rest of the car is pretty quiet at that point.

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